Next, note that \(\tilde{X}\)  is obtained by classically processing a measurement outcome \(a\)  of the quantum state \(\rho _{\mathcal {E}_X}\)  The data processing inequality and Holevo's theorem [1]}, [2]}, [3]}, [4]} then imply
\( I(X : \tilde{X}) \le I(X : a) \le \chi (X : \rho _{\operatorname{{\mathcal {E}}}_X}).\) 
